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glibc/sysdeps/ia64/fpu/s_asinhf.S
Siddhesh Poyarekar 30891f35fa Remove "Contributed by" lines 
We stopped adding "Contributed by" or similar lines in sources in 2012
in favour of git logs and keeping the Contributors section of the
glibc manual up to date.  Removing these lines makes the license
header a bit more consistent across files and also removes the
possibility of error in attribution when license blocks or files are
copied across since the contributed-by lines don't actually reflect
reality in those cases.

Move all "Contributed by" and similar lines (Written by, Test by,
etc.) into a new file CONTRIBUTED-BY to retain record of these
contributions.  These contributors are also mentioned in
manual/contrib.texi, so we just maintain this additional record as a
courtesy to the earlier developers.

The following scripts were used to filter a list of files to edit in
place and to clean up the CONTRIBUTED-BY file respectively.  These
were not added to the glibc sources because they're not expected to be
of any use in future given that this is a one time task:

https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc
https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02

Reviewed-by: Carlos O'Donell <carlos@redhat.com>
2021-09-03 22:06:44 +05:30

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.file "asinhf.s"
// Copyright (c) 2000 - 2003, Intel Corporation
// All rights reserved.
//
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// ==============================================================
// History
// ==============================================================
// 04/02/01 Initial version
// 04/19/01 Improved speed of the paths #1,2,3,4,5
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/06/03 Reordered header: .section, .global, .proc, .align
// 05/21/03 Improved performance, fixed to handle unorms
//
// API
// ==============================================================
// float asinhf(float)
//
// Overview of operation
// ==============================================================
//
// There are 7 paths:
// 1. x = 0.0
// Return asinhf(x) = 0.0
// 2. 0.0 <|x| < 2^(-5)
// Return asinhf(x) = Pol5(x), where Pol5(x) = ((x^2)*C1 + C0)*x^3 + x
// 3. 2^(-5) <= |x| < 2^51
// Return asinhf(x) = sign(x)*(log(|x| + sqrt(x^2 + 1.0)))
// To compute x + sqrt(x^2 + 1.0) modified Newton Raphson method is used
// (2 iterations)
// Algorithm description for log function see below.
//
// 4. 2^51 <= |x| < +INF
// Return asinhf(x) = sign(x)*log(2*|x|)
// Algorithm description for log function see below.
//
// 5. x = INF
// Return asinhf(x) = INF
//
// 6. x = [S,Q]NaN
// Return asinhf(x) = QNaN
//
// 7. x = denormal
// Return asinhf(x) = x
//
//==============================================================
// Algorithm Description for log(x) function
// Below we are using the fact that inequality x - 1.0 > 2^(-6) is always
// true for this asinh implementation
//
// Consider x = 2^N 1.f1 f2 f3 f4...f63
// Log(x) = log(frcpa(x) x/frcpa(x))
// = log(1/frcpa(x)) + log(frcpa(x) x)
// = -log(frcpa(x)) + log(frcpa(x) x)
//
// frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)
//
// -log(frcpa(x)) = -log(C)
// = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
//
// -log(frcpa(x)) = -log(C)
// = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
//
// -log(frcpa(x)) = -log(C)
// = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
//
// Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
//
// Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
// Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
// Log(x) = +Nlog2 + T + log(frcpa(x) x)
//
// Log(x) = +Nlog2 + T + log(C x)
//
// Cx = 1 + r
//
// Log(x) = +Nlog2 + T + log(1+r)
// Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....)
//
// 1.f1 f2 ... f8 has 256 entries.
// They are 1 + k/2^8, k = 0 ... 255
// These 256 values are the table entries.
//
// Implementation
//==============================================================
// C = frcpa(x)
// r = C * x - 1
//
// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4
//
// x = f * 2*n where f is 1.f_1f_2f_3....f_63
// Nfloat = float(n) where n is the true unbiased exponent
// pre-index = f_1f_2....f_8
// index = pre_index * 8
// get the dxt table entry at index + offset = T
//
// result = (T + Nfloat * log(2)) + rseries
//
// The T table is calculated as follows
// Form x_k = 1 + k/2^8 where k goes from 0... 255
// y_k = frcpa(x_k)
// log(1/y_k) in quad and round to double-extended
//
//
// Registers used
//==============================================================
// Floating Point registers used:
// f8, input
// f9 -> f15, f32 -> f55
// General registers used:
// r14 -> r27
// Predicate registers used:
// p6 -> p14
// p6 to filter out case when x = [Q,S]NaN or INF or zero
// p7 to filter out case when x < 0.0
// p8 to select path #2
// p11 to filter out case when x >= 0
// p12 to filter out case when x = + denormal
// p13 to select path #4
// p14 to filtef out case when x = - denormal
// Assembly macros
//==============================================================
log_GR_exp_17_ones = r14
log_GR_signexp_f8 = r15
log_table_address2 = r16
log_GR_exp_16_ones = r17
log_GR_exp_f8 = r18
log_GR_true_exp_f8 = r19
log_GR_significand_f8 = r20
log_GR_index = r21
log_GR_comp2 = r22
asinh_GR_f8 = r23
asinh_GR_comp = r24
asinh_GR_f8 = r25
log_table_address3 = r26
NR_table_address = r27
//==============================================================
log_y = f9
NR1 = f10
NR2 = f11
log_y_rs = f12
log_y_rs_iter = f13
log_y_rs_iter1 = f14
fNormX = f15
asinh_w_sq = f32
log_arg_early = f33
log_y_rs_iter2 = f34
log_P3 = f35
log_P2 = f36
log_P1 = f37
log2 = f38
log_C0 = f39
log_C1 = f40
asinh_f8 = f41
log_C = f42
log_arg = f43
asinh_w_cube = f44
log_int_Nfloat = f45
log_r = f46
log_rsq = f47
asinh_w_1 = f48
log_rp_p32 = f49
log_rcube = f50
log_rp_p10 = f51
log_rp_p2 = f52
log_Nfloat = f53
log_T = f54
log_T_plus_Nlog2 = f55
// Data tables
//==============================================================
RODATA
.align 16
LOCAL_OBJECT_START(log_table_1)
data8 0xbfd0001008f39d59 // p3
data8 0x3fd5556073e0c45a // p2
data8 0xbfdffffffffaea15 // p1
data8 0x3fe62e42fefa39ef // log(2)
LOCAL_OBJECT_END(log_table_1)
LOCAL_OBJECT_START(log_table_2)
data8 0x3FE0000000000000 // 0.5
data8 0x4008000000000000 // 3.0
data8 0x9979C79685A5EB16, 0x00003FFB // C1 3FFB9979C79685A5EB16
data8 0xAAAAA96F80786D62, 0x0000BFFC // C0 BFFCAAAAA96F80786D62
LOCAL_OBJECT_END(log_table_2)
LOCAL_OBJECT_START(log_table_3)
data8 0x3F60040155D5889E //log(1/frcpa(1+ 0/256)
data8 0x3F78121214586B54 //log(1/frcpa(1+ 1/256)
data8 0x3F841929F96832F0 //log(1/frcpa(1+ 2/256)
data8 0x3F8C317384C75F06 //log(1/frcpa(1+ 3/256)
data8 0x3F91A6B91AC73386 //log(1/frcpa(1+ 4/256)
data8 0x3F95BA9A5D9AC039 //log(1/frcpa(1+ 5/256)
data8 0x3F99D2A8074325F4 //log(1/frcpa(1+ 6/256)
data8 0x3F9D6B2725979802 //log(1/frcpa(1+ 7/256)
data8 0x3FA0C58FA19DFAAA //log(1/frcpa(1+ 8/256)
data8 0x3FA2954C78CBCE1B //log(1/frcpa(1+ 9/256)
data8 0x3FA4A94D2DA96C56 //log(1/frcpa(1+ 10/256)
data8 0x3FA67C94F2D4BB58 //log(1/frcpa(1+ 11/256)
data8 0x3FA85188B630F068 //log(1/frcpa(1+ 12/256)
data8 0x3FAA6B8ABE73AF4C //log(1/frcpa(1+ 13/256)
data8 0x3FAC441E06F72A9E //log(1/frcpa(1+ 14/256)
data8 0x3FAE1E6713606D07 //log(1/frcpa(1+ 15/256)
data8 0x3FAFFA6911AB9301 //log(1/frcpa(1+ 16/256)
data8 0x3FB0EC139C5DA601 //log(1/frcpa(1+ 17/256)
data8 0x3FB1DBD2643D190B //log(1/frcpa(1+ 18/256)
data8 0x3FB2CC7284FE5F1C //log(1/frcpa(1+ 19/256)
data8 0x3FB3BDF5A7D1EE64 //log(1/frcpa(1+ 20/256)
data8 0x3FB4B05D7AA012E0 //log(1/frcpa(1+ 21/256)
data8 0x3FB580DB7CEB5702 //log(1/frcpa(1+ 22/256)
data8 0x3FB674F089365A7A //log(1/frcpa(1+ 23/256)
data8 0x3FB769EF2C6B568D //log(1/frcpa(1+ 24/256)
data8 0x3FB85FD927506A48 //log(1/frcpa(1+ 25/256)
data8 0x3FB9335E5D594989 //log(1/frcpa(1+ 26/256)
data8 0x3FBA2B0220C8E5F5 //log(1/frcpa(1+ 27/256)
data8 0x3FBB0004AC1A86AC //log(1/frcpa(1+ 28/256)
data8 0x3FBBF968769FCA11 //log(1/frcpa(1+ 29/256)
data8 0x3FBCCFEDBFEE13A8 //log(1/frcpa(1+ 30/256)
data8 0x3FBDA727638446A2 //log(1/frcpa(1+ 31/256)
data8 0x3FBEA3257FE10F7A //log(1/frcpa(1+ 32/256)
data8 0x3FBF7BE9FEDBFDE6 //log(1/frcpa(1+ 33/256)
data8 0x3FC02AB352FF25F4 //log(1/frcpa(1+ 34/256)
data8 0x3FC097CE579D204D //log(1/frcpa(1+ 35/256)
data8 0x3FC1178E8227E47C //log(1/frcpa(1+ 36/256)
data8 0x3FC185747DBECF34 //log(1/frcpa(1+ 37/256)
data8 0x3FC1F3B925F25D41 //log(1/frcpa(1+ 38/256)
data8 0x3FC2625D1E6DDF57 //log(1/frcpa(1+ 39/256)
data8 0x3FC2D1610C86813A //log(1/frcpa(1+ 40/256)
data8 0x3FC340C59741142E //log(1/frcpa(1+ 41/256)
data8 0x3FC3B08B6757F2A9 //log(1/frcpa(1+ 42/256)
data8 0x3FC40DFB08378003 //log(1/frcpa(1+ 43/256)
data8 0x3FC47E74E8CA5F7C //log(1/frcpa(1+ 44/256)
data8 0x3FC4EF51F6466DE4 //log(1/frcpa(1+ 45/256)
data8 0x3FC56092E02BA516 //log(1/frcpa(1+ 46/256)
data8 0x3FC5D23857CD74D5 //log(1/frcpa(1+ 47/256)
data8 0x3FC6313A37335D76 //log(1/frcpa(1+ 48/256)
data8 0x3FC6A399DABBD383 //log(1/frcpa(1+ 49/256)
data8 0x3FC70337DD3CE41B //log(1/frcpa(1+ 50/256)
data8 0x3FC77654128F6127 //log(1/frcpa(1+ 51/256)
data8 0x3FC7E9D82A0B022D //log(1/frcpa(1+ 52/256)
data8 0x3FC84A6B759F512F //log(1/frcpa(1+ 53/256)
data8 0x3FC8AB47D5F5A310 //log(1/frcpa(1+ 54/256)
data8 0x3FC91FE49096581B //log(1/frcpa(1+ 55/256)
data8 0x3FC981634011AA75 //log(1/frcpa(1+ 56/256)
data8 0x3FC9F6C407089664 //log(1/frcpa(1+ 57/256)
data8 0x3FCA58E729348F43 //log(1/frcpa(1+ 58/256)
data8 0x3FCABB55C31693AD //log(1/frcpa(1+ 59/256)
data8 0x3FCB1E104919EFD0 //log(1/frcpa(1+ 60/256)
data8 0x3FCB94EE93E367CB //log(1/frcpa(1+ 61/256)
data8 0x3FCBF851C067555F //log(1/frcpa(1+ 62/256)
data8 0x3FCC5C0254BF23A6 //log(1/frcpa(1+ 63/256)
data8 0x3FCCC000C9DB3C52 //log(1/frcpa(1+ 64/256)
data8 0x3FCD244D99C85674 //log(1/frcpa(1+ 65/256)
data8 0x3FCD88E93FB2F450 //log(1/frcpa(1+ 66/256)
data8 0x3FCDEDD437EAEF01 //log(1/frcpa(1+ 67/256)
data8 0x3FCE530EFFE71012 //log(1/frcpa(1+ 68/256)
data8 0x3FCEB89A1648B971 //log(1/frcpa(1+ 69/256)
data8 0x3FCF1E75FADF9BDE //log(1/frcpa(1+ 70/256)
data8 0x3FCF84A32EAD7C35 //log(1/frcpa(1+ 71/256)
data8 0x3FCFEB2233EA07CD //log(1/frcpa(1+ 72/256)
data8 0x3FD028F9C7035C1C //log(1/frcpa(1+ 73/256)
data8 0x3FD05C8BE0D9635A //log(1/frcpa(1+ 74/256)
data8 0x3FD085EB8F8AE797 //log(1/frcpa(1+ 75/256)
data8 0x3FD0B9C8E32D1911 //log(1/frcpa(1+ 76/256)
data8 0x3FD0EDD060B78081 //log(1/frcpa(1+ 77/256)
data8 0x3FD122024CF0063F //log(1/frcpa(1+ 78/256)
data8 0x3FD14BE2927AECD4 //log(1/frcpa(1+ 79/256)
data8 0x3FD180618EF18ADF //log(1/frcpa(1+ 80/256)
data8 0x3FD1B50BBE2FC63B //log(1/frcpa(1+ 81/256)
data8 0x3FD1DF4CC7CF242D //log(1/frcpa(1+ 82/256)
data8 0x3FD214456D0EB8D4 //log(1/frcpa(1+ 83/256)
data8 0x3FD23EC5991EBA49 //log(1/frcpa(1+ 84/256)
data8 0x3FD2740D9F870AFB //log(1/frcpa(1+ 85/256)
data8 0x3FD29ECDABCDFA04 //log(1/frcpa(1+ 86/256)
data8 0x3FD2D46602ADCCEE //log(1/frcpa(1+ 87/256)
data8 0x3FD2FF66B04EA9D4 //log(1/frcpa(1+ 88/256)
data8 0x3FD335504B355A37 //log(1/frcpa(1+ 89/256)
data8 0x3FD360925EC44F5D //log(1/frcpa(1+ 90/256)
data8 0x3FD38BF1C3337E75 //log(1/frcpa(1+ 91/256)
data8 0x3FD3C25277333184 //log(1/frcpa(1+ 92/256)
data8 0x3FD3EDF463C1683E //log(1/frcpa(1+ 93/256)
data8 0x3FD419B423D5E8C7 //log(1/frcpa(1+ 94/256)
data8 0x3FD44591E0539F49 //log(1/frcpa(1+ 95/256)
data8 0x3FD47C9175B6F0AD //log(1/frcpa(1+ 96/256)
data8 0x3FD4A8B341552B09 //log(1/frcpa(1+ 97/256)
data8 0x3FD4D4F3908901A0 //log(1/frcpa(1+ 98/256)
data8 0x3FD501528DA1F968 //log(1/frcpa(1+ 99/256)
data8 0x3FD52DD06347D4F6 //log(1/frcpa(1+ 100/256)
data8 0x3FD55A6D3C7B8A8A //log(1/frcpa(1+ 101/256)
data8 0x3FD5925D2B112A59 //log(1/frcpa(1+ 102/256)
data8 0x3FD5BF406B543DB2 //log(1/frcpa(1+ 103/256)
data8 0x3FD5EC433D5C35AE //log(1/frcpa(1+ 104/256)
data8 0x3FD61965CDB02C1F //log(1/frcpa(1+ 105/256)
data8 0x3FD646A84935B2A2 //log(1/frcpa(1+ 106/256)
data8 0x3FD6740ADD31DE94 //log(1/frcpa(1+ 107/256)
data8 0x3FD6A18DB74A58C5 //log(1/frcpa(1+ 108/256)
data8 0x3FD6CF31058670EC //log(1/frcpa(1+ 109/256)
data8 0x3FD6F180E852F0BA //log(1/frcpa(1+ 110/256)
data8 0x3FD71F5D71B894F0 //log(1/frcpa(1+ 111/256)
data8 0x3FD74D5AEFD66D5C //log(1/frcpa(1+ 112/256)
data8 0x3FD77B79922BD37E //log(1/frcpa(1+ 113/256)
data8 0x3FD7A9B9889F19E2 //log(1/frcpa(1+ 114/256)
data8 0x3FD7D81B037EB6A6 //log(1/frcpa(1+ 115/256)
data8 0x3FD8069E33827231 //log(1/frcpa(1+ 116/256)
data8 0x3FD82996D3EF8BCB //log(1/frcpa(1+ 117/256)
data8 0x3FD85855776DCBFB //log(1/frcpa(1+ 118/256)
data8 0x3FD8873658327CCF //log(1/frcpa(1+ 119/256)
data8 0x3FD8AA75973AB8CF //log(1/frcpa(1+ 120/256)
data8 0x3FD8D992DC8824E5 //log(1/frcpa(1+ 121/256)
data8 0x3FD908D2EA7D9512 //log(1/frcpa(1+ 122/256)
data8 0x3FD92C59E79C0E56 //log(1/frcpa(1+ 123/256)
data8 0x3FD95BD750EE3ED3 //log(1/frcpa(1+ 124/256)
data8 0x3FD98B7811A3EE5B //log(1/frcpa(1+ 125/256)
data8 0x3FD9AF47F33D406C //log(1/frcpa(1+ 126/256)
data8 0x3FD9DF270C1914A8 //log(1/frcpa(1+ 127/256)
data8 0x3FDA0325ED14FDA4 //log(1/frcpa(1+ 128/256)
data8 0x3FDA33440224FA79 //log(1/frcpa(1+ 129/256)
data8 0x3FDA57725E80C383 //log(1/frcpa(1+ 130/256)
data8 0x3FDA87D0165DD199 //log(1/frcpa(1+ 131/256)
data8 0x3FDAAC2E6C03F896 //log(1/frcpa(1+ 132/256)
data8 0x3FDADCCC6FDF6A81 //log(1/frcpa(1+ 133/256)
data8 0x3FDB015B3EB1E790 //log(1/frcpa(1+ 134/256)
data8 0x3FDB323A3A635948 //log(1/frcpa(1+ 135/256)
data8 0x3FDB56FA04462909 //log(1/frcpa(1+ 136/256)
data8 0x3FDB881AA659BC93 //log(1/frcpa(1+ 137/256)
data8 0x3FDBAD0BEF3DB165 //log(1/frcpa(1+ 138/256)
data8 0x3FDBD21297781C2F //log(1/frcpa(1+ 139/256)
data8 0x3FDC039236F08819 //log(1/frcpa(1+ 140/256)
data8 0x3FDC28CB1E4D32FD //log(1/frcpa(1+ 141/256)
data8 0x3FDC4E19B84723C2 //log(1/frcpa(1+ 142/256)
data8 0x3FDC7FF9C74554C9 //log(1/frcpa(1+ 143/256)
data8 0x3FDCA57B64E9DB05 //log(1/frcpa(1+ 144/256)
data8 0x3FDCCB130A5CEBB0 //log(1/frcpa(1+ 145/256)
data8 0x3FDCF0C0D18F326F //log(1/frcpa(1+ 146/256)
data8 0x3FDD232075B5A201 //log(1/frcpa(1+ 147/256)
data8 0x3FDD490246DEFA6B //log(1/frcpa(1+ 148/256)
data8 0x3FDD6EFA918D25CD //log(1/frcpa(1+ 149/256)
data8 0x3FDD9509707AE52F //log(1/frcpa(1+ 150/256)
data8 0x3FDDBB2EFE92C554 //log(1/frcpa(1+ 151/256)
data8 0x3FDDEE2F3445E4AF //log(1/frcpa(1+ 152/256)
data8 0x3FDE148A1A2726CE //log(1/frcpa(1+ 153/256)
data8 0x3FDE3AFC0A49FF40 //log(1/frcpa(1+ 154/256)
data8 0x3FDE6185206D516E //log(1/frcpa(1+ 155/256)
data8 0x3FDE882578823D52 //log(1/frcpa(1+ 156/256)
data8 0x3FDEAEDD2EAC990C //log(1/frcpa(1+ 157/256)
data8 0x3FDED5AC5F436BE3 //log(1/frcpa(1+ 158/256)
data8 0x3FDEFC9326D16AB9 //log(1/frcpa(1+ 159/256)
data8 0x3FDF2391A2157600 //log(1/frcpa(1+ 160/256)
data8 0x3FDF4AA7EE03192D //log(1/frcpa(1+ 161/256)
data8 0x3FDF71D627C30BB0 //log(1/frcpa(1+ 162/256)
data8 0x3FDF991C6CB3B379 //log(1/frcpa(1+ 163/256)
data8 0x3FDFC07ADA69A910 //log(1/frcpa(1+ 164/256)
data8 0x3FDFE7F18EB03D3E //log(1/frcpa(1+ 165/256)
data8 0x3FE007C053C5002E //log(1/frcpa(1+ 166/256)
data8 0x3FE01B942198A5A1 //log(1/frcpa(1+ 167/256)
data8 0x3FE02F74400C64EB //log(1/frcpa(1+ 168/256)
data8 0x3FE04360BE7603AD //log(1/frcpa(1+ 169/256)
data8 0x3FE05759AC47FE34 //log(1/frcpa(1+ 170/256)
data8 0x3FE06B5F1911CF52 //log(1/frcpa(1+ 171/256)
data8 0x3FE078BF0533C568 //log(1/frcpa(1+ 172/256)
data8 0x3FE08CD9687E7B0E //log(1/frcpa(1+ 173/256)
data8 0x3FE0A10074CF9019 //log(1/frcpa(1+ 174/256)
data8 0x3FE0B5343A234477 //log(1/frcpa(1+ 175/256)
data8 0x3FE0C974C89431CE //log(1/frcpa(1+ 176/256)
data8 0x3FE0DDC2305B9886 //log(1/frcpa(1+ 177/256)
data8 0x3FE0EB524BAFC918 //log(1/frcpa(1+ 178/256)
data8 0x3FE0FFB54213A476 //log(1/frcpa(1+ 179/256)
data8 0x3FE114253DA97D9F //log(1/frcpa(1+ 180/256)
data8 0x3FE128A24F1D9AFF //log(1/frcpa(1+ 181/256)
data8 0x3FE1365252BF0865 //log(1/frcpa(1+ 182/256)
data8 0x3FE14AE558B4A92D //log(1/frcpa(1+ 183/256)
data8 0x3FE15F85A19C765B //log(1/frcpa(1+ 184/256)
data8 0x3FE16D4D38C119FA //log(1/frcpa(1+ 185/256)
data8 0x3FE18203C20DD133 //log(1/frcpa(1+ 186/256)
data8 0x3FE196C7BC4B1F3B //log(1/frcpa(1+ 187/256)
data8 0x3FE1A4A738B7A33C //log(1/frcpa(1+ 188/256)
data8 0x3FE1B981C0C9653D //log(1/frcpa(1+ 189/256)
data8 0x3FE1CE69E8BB106B //log(1/frcpa(1+ 190/256)
data8 0x3FE1DC619DE06944 //log(1/frcpa(1+ 191/256)
data8 0x3FE1F160A2AD0DA4 //log(1/frcpa(1+ 192/256)
data8 0x3FE2066D7740737E //log(1/frcpa(1+ 193/256)
data8 0x3FE2147DBA47A394 //log(1/frcpa(1+ 194/256)
data8 0x3FE229A1BC5EBAC3 //log(1/frcpa(1+ 195/256)
data8 0x3FE237C1841A502E //log(1/frcpa(1+ 196/256)
data8 0x3FE24CFCE6F80D9A //log(1/frcpa(1+ 197/256)
data8 0x3FE25B2C55CD5762 //log(1/frcpa(1+ 198/256)
data8 0x3FE2707F4D5F7C41 //log(1/frcpa(1+ 199/256)
data8 0x3FE285E0842CA384 //log(1/frcpa(1+ 200/256)
data8 0x3FE294294708B773 //log(1/frcpa(1+ 201/256)
data8 0x3FE2A9A2670AFF0C //log(1/frcpa(1+ 202/256)
data8 0x3FE2B7FB2C8D1CC1 //log(1/frcpa(1+ 203/256)
data8 0x3FE2C65A6395F5F5 //log(1/frcpa(1+ 204/256)
data8 0x3FE2DBF557B0DF43 //log(1/frcpa(1+ 205/256)
data8 0x3FE2EA64C3F97655 //log(1/frcpa(1+ 206/256)
data8 0x3FE3001823684D73 //log(1/frcpa(1+ 207/256)
data8 0x3FE30E97E9A8B5CD //log(1/frcpa(1+ 208/256)
data8 0x3FE32463EBDD34EA //log(1/frcpa(1+ 209/256)
data8 0x3FE332F4314AD796 //log(1/frcpa(1+ 210/256)
data8 0x3FE348D90E7464D0 //log(1/frcpa(1+ 211/256)
data8 0x3FE35779F8C43D6E //log(1/frcpa(1+ 212/256)
data8 0x3FE36621961A6A99 //log(1/frcpa(1+ 213/256)
data8 0x3FE37C299F3C366A //log(1/frcpa(1+ 214/256)
data8 0x3FE38AE2171976E7 //log(1/frcpa(1+ 215/256)
data8 0x3FE399A157A603E7 //log(1/frcpa(1+ 216/256)
data8 0x3FE3AFCCFE77B9D1 //log(1/frcpa(1+ 217/256)
data8 0x3FE3BE9D503533B5 //log(1/frcpa(1+ 218/256)
data8 0x3FE3CD7480B4A8A3 //log(1/frcpa(1+ 219/256)
data8 0x3FE3E3C43918F76C //log(1/frcpa(1+ 220/256)
data8 0x3FE3F2ACB27ED6C7 //log(1/frcpa(1+ 221/256)
data8 0x3FE4019C2125CA93 //log(1/frcpa(1+ 222/256)
data8 0x3FE4181061389722 //log(1/frcpa(1+ 223/256)
data8 0x3FE42711518DF545 //log(1/frcpa(1+ 224/256)
data8 0x3FE436194E12B6BF //log(1/frcpa(1+ 225/256)
data8 0x3FE445285D68EA69 //log(1/frcpa(1+ 226/256)
data8 0x3FE45BCC464C893A //log(1/frcpa(1+ 227/256)
data8 0x3FE46AED21F117FC //log(1/frcpa(1+ 228/256)
data8 0x3FE47A1527E8A2D3 //log(1/frcpa(1+ 229/256)
data8 0x3FE489445EFFFCCC //log(1/frcpa(1+ 230/256)
data8 0x3FE4A018BCB69835 //log(1/frcpa(1+ 231/256)
data8 0x3FE4AF5A0C9D65D7 //log(1/frcpa(1+ 232/256)
data8 0x3FE4BEA2A5BDBE87 //log(1/frcpa(1+ 233/256)
data8 0x3FE4CDF28F10AC46 //log(1/frcpa(1+ 234/256)
data8 0x3FE4DD49CF994058 //log(1/frcpa(1+ 235/256)
data8 0x3FE4ECA86E64A684 //log(1/frcpa(1+ 236/256)
data8 0x3FE503C43CD8EB68 //log(1/frcpa(1+ 237/256)
data8 0x3FE513356667FC57 //log(1/frcpa(1+ 238/256)
data8 0x3FE522AE0738A3D8 //log(1/frcpa(1+ 239/256)
data8 0x3FE5322E26867857 //log(1/frcpa(1+ 240/256)
data8 0x3FE541B5CB979809 //log(1/frcpa(1+ 241/256)
data8 0x3FE55144FDBCBD62 //log(1/frcpa(1+ 242/256)
data8 0x3FE560DBC45153C7 //log(1/frcpa(1+ 243/256)
data8 0x3FE5707A26BB8C66 //log(1/frcpa(1+ 244/256)
data8 0x3FE587F60ED5B900 //log(1/frcpa(1+ 245/256)
data8 0x3FE597A7977C8F31 //log(1/frcpa(1+ 246/256)
data8 0x3FE5A760D634BB8B //log(1/frcpa(1+ 247/256)
data8 0x3FE5B721D295F10F //log(1/frcpa(1+ 248/256)
data8 0x3FE5C6EA94431EF9 //log(1/frcpa(1+ 249/256)
data8 0x3FE5D6BB22EA86F6 //log(1/frcpa(1+ 250/256)
data8 0x3FE5E6938645D390 //log(1/frcpa(1+ 251/256)
data8 0x3FE5F673C61A2ED2 //log(1/frcpa(1+ 252/256)
data8 0x3FE6065BEA385926 //log(1/frcpa(1+ 253/256)
data8 0x3FE6164BFA7CC06B //log(1/frcpa(1+ 254/256)
data8 0x3FE62643FECF9743 //log(1/frcpa(1+ 255/256)
LOCAL_OBJECT_END(log_table_3)
.section .text
GLOBAL_LIBM_ENTRY(asinhf)
{ .mfi
getf.exp asinh_GR_f8 = f8 // Must recompute later if x unorm
fclass.m p12,p0 = f8, 0x0b // Test x unorm
mov log_GR_exp_17_ones = 0x1ffff
}
{ .mfi
addl NR_table_address = @ltoff(log_table_1), gp
fma.s1 log_y = f8, f8, f1 // y = x^2 + 1
mov asinh_GR_comp = 0xfffa
}
;;
{ .mfi
mov log_GR_exp_16_ones = 0xffff //BIAS
fclass.m p6,p0 = f8, 0xe7 // Test for x = NaN and inf and zero
mov log_GR_comp2 = 0x10032
}
{ .mfi
ld8 NR_table_address = [NR_table_address]
fma.s1 asinh_w_sq = f8,f8,f0 // x^2
nop.i 0
}
;;
{ .mfi
nop.m 0
fcmp.lt.s1 p7,p11 = f8,f0 // if x<0
nop.i 0
}
{ .mfb
nop.m 0
fnorm.s1 fNormX = f8 // Normalize x
(p12) br.cond.spnt ASINH_UNORM // Branch if x=unorm
}
;;
ASINH_COMMON:
// Return here if x=unorm and not denorm
{ .mfi
//to get second table address
adds log_table_address2 = 0x20, NR_table_address
fma.s1 log_arg = f8,f1,f8
}
{ .mfb
nop.m 0
(p6) fma.s.s0 f8 = f8,f1,f8 // quietize nan result if x=nan
(p6) br.ret.spnt b0 // Exit for x=nan and inf and zero
}
;;
{ .mfi
ldfpd NR1,NR2 = [log_table_address2],16
frsqrta.s1 log_y_rs,p0 = log_y // z=1/sqrt(y)
nop.i 0
}
;;
{ .mfi
ldfe log_C1 = [log_table_address2],16
nop.f 0
and asinh_GR_f8 = asinh_GR_f8,log_GR_exp_17_ones
}
;;
{ .mib
ldfe log_C0 = [log_table_address2],16
cmp.le p13,p0 = log_GR_comp2,asinh_GR_f8
(p13) br.cond.spnt LOG_COMMON1 // Branch if path 4: |x| >= 2^51
}
;;
{ .mfi
nop.m 0
fma.s1 log_y_rs_iter = log_y_rs,log_y,f0 // y*z
nop.i 0
}
;;
.pred.rel "mutex",p7,p11
{ .mfi
nop.m 0
(p11) mov asinh_f8 = fNormX
nop.i 0
}
{ .mfb
cmp.gt p8,p0 = asinh_GR_comp,asinh_GR_f8
(p7) fnma.s1 asinh_f8 = fNormX,f1,f0
(p8) br.cond.spnt ASINH_NEAR_ZERO // Branch if path 2: 0 < |x| < 2^-5
}
;;
// Here if main path, 2^-5 <= |x| < 2^51
///////////////////////////////// The first iteration /////////////////////////
{ .mfi
ldfpd log_P3,log_P2 = [NR_table_address],16
fnma.s1 log_y_rs_iter2 = log_y_rs_iter,log_y_rs,NR2 // 3-(y*z)*z
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_y_rs_iter1 = log_y_rs,NR1,f0 // 0.5*z
nop.i 0
}
;;
{ .mfi
ldfpd log_P1,log2 = [NR_table_address],16
// (0.5*z)*(3-(y*z)*z)
fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs_iter2,f0
nop.i 0
}
{ .mfi
nop.m 0
// (0.5*z)*(3-(y*z)*z)
fma.s1 log_arg_early = log_y_rs_iter1,log_y_rs_iter2,f0
nop.i 0
}
;;
////////////////////////////////// The second iteration ////////////////////////
{ .mfi
nop.m 0
fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_arg_early = log_arg_early,log_y,asinh_f8
nop.i 0
}
;;
{ .mfi
nop.m 0
fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_y_rs_iter1 = log_y_rs_iter1,log_y,f0
nop.i 0
}
;;
{ .mfi
nop.m 0
frcpa.s1 log_C,p0 = f1,log_arg_early
nop.i 0
}
;;
{ .mfi
getf.exp log_GR_signexp_f8 = log_arg_early
nop.f 0
nop.i 0
}
;;
{ .mfi
getf.sig log_GR_significand_f8 = log_arg_early
// (0.5*z)*(3-(y*z)*z)*y + |x|
fma.s1 log_arg = log_y_rs_iter1,log_y_rs,asinh_f8
//to get third table address
adds log_table_address3 = 0x30, NR_table_address
}
;;
/////////////////////////////////////////// The end NR iterations /////////////
{ .mfi
nop.m 0
nop.f 0
//significant bit destruction
and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
}
;;
{ .mfi
//BIAS subtraction
sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
(p7) fnma.s1 log2 = log2,f1,f0
nop.i 0
}
;;
{ .mfi
setf.sig log_int_Nfloat = log_GR_true_exp_f8
fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1
extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
}
;;
{ .mmi
//pre-index*16 + index
shladd log_table_address3 = log_GR_index,3,log_table_address3
;;
ldfd log_T = [log_table_address3]
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_rsq = log_r, log_r, f0 //r^2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_rp_p10 = log_P1, log_r, f1
nop.i 0
}
;;
{ .mfi
nop.m 0
//convert N to the floating-point format
fcvt.xf log_Nfloat = log_int_Nfloat
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10
nop.i 0
}
;;
.pred.rel "mutex",p7,p11
{ .mfi
nop.m 0
(p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0
nop.i 0
}
{ .mfi
nop.m 0
(p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0
nop.i 0
}
;;
{ .mfi
nop.m 0
(p11) fma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
nop.i 0
}
{ .mfb
nop.m 0
(p7) fnma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
br.ret.sptk b0 // Exit main path, path 3: 2^-5 <= |x| < 2^51
}
;;
// Here if path 4, |x| >= 2^51
LOG_COMMON1:
{ .mfi
ldfpd log_P3,log_P2 = [NR_table_address],16
nop.f 0
nop.i 0
}
;;
{ .mfi
ldfpd log_P1,log2 = [NR_table_address],16
frcpa.s1 log_C,p0 = f1,log_arg
nop.i 0
}
;;
{ .mfi
getf.exp log_GR_signexp_f8 = log_arg
nop.f 0
//to get third table address
adds log_table_address3 = 0x30, NR_table_address
}
;;
{ .mfi
getf.sig log_GR_significand_f8 = log_arg
nop.f 0
nop.i 0
}
;;
{ .mfi
nop.m 0
nop.f 0
//to destroy the most bit in the significant area
and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
}
;;
{ .mmf
nop.m 0
//BIAS subtraction
sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1
}
;;
{ .mfi
setf.sig log_int_Nfloat = log_GR_true_exp_f8
nop.f 0
extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
}
;;
{ .mmi
//pre-index*16 + index
shladd log_table_address3 = log_GR_index,3,log_table_address3
;;
ldfd log_T = [log_table_address3]
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_rsq = log_r, log_r, f0 //r^2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_rp_p10 = log_P1, log_r, f1
nop.i 0
}
{ .mfi
nop.m 0
(p7) fnma.s1 log2 = log2,f1,f0
nop.i 0
}
;;
{ .mfi
nop.m 0
//convert N to the floating-point format
fcvt.xf log_Nfloat = log_int_Nfloat
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10
nop.i 0
}
;;
.pred.rel "mutex",p7,p11
{ .mfi
nop.m 0
(p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0
nop.i 0
}
{ .mfi
nop.m 0
(p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0
nop.i 0
}
;;
{ .mfi
nop.m 0
(p11) fma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
nop.i 0
}
{ .mfb
nop.m 0
(p7) fnma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
br.ret.sptk b0 // Exit path 4, |x| >= 2^51
}
;;
// Here if path 2, 0 < |x| < 2^-5
ASINH_NEAR_ZERO:
{ .mfi
nop.m 0
fma.s1 asinh_w_1 = asinh_w_sq,log_C1,log_C0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 asinh_w_cube = asinh_w_sq,fNormX,f0
nop.i 0
}
;;
{ .mfb
nop.m 0
fma.s.s0 f8 = asinh_w_1,asinh_w_cube,fNormX
br.ret.sptk b0 // Exit path 2, 0 < |x| < 2^-5
}
;;
ASINH_UNORM:
// Here if x=unorm
{ .mfi
getf.exp asinh_GR_f8 = fNormX // Recompute if x unorm
fclass.m p0,p13 = fNormX, 0x0b // Test x denorm
nop.i 0
}
;;
{ .mfb
nop.m 0
fcmp.eq.s0 p14,p0 = f8, f0 // Dummy to set denormal flag
(p13) br.cond.sptk ASINH_COMMON // Continue if x unorm and not denorm
}
;;
.pred.rel "mutex",p7,p11
{ .mfi
nop.m 0
(p7) fma.s.s0 f8 = f8,f8,f8 // Result x+x^2 if x=-denorm
nop.i 0
}
{ .mfb
nop.m 0
(p11) fnma.s.s0 f8 = f8,f8,f8 // Result x-x^2 if x=+denorm
br.ret.spnt b0 // Exit if denorm
}
;;
GLOBAL_LIBM_END(asinhf)
libm_alias_float_other (asinh, asinh)
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